Kravchuk K. Statistical properties of impulse neurons activity in presence of delayed feedback

The influence of the delayed feedback presence on neuronal firing statistics is studied. Single neuron with delayed feedback under Poisson stimulation is considered. Rigorous analytical expressions are otained for single-interspike intervals (ISI) and multiple-ISI probability densities, and for the mean ISI duration and ISI coefficient of variation. It is shown, that the delayed feedback presence results in prominent peculiarities in the single-ISI probability density, and also leads to substantial increase in ISI coefficient of variation, as compared to the case of no feedback. It is proven, that the delayed feedback presence results in non-Markovian statistics of neuronal firing.